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I have the following information:
\[n=p^2q\]
\[k \ge 4\]
\[0<v<n\]
\[0 \le x < pq\]
\[y=\lceil \frac{(vx^k) \mod n}{pq} \rceil \cdot (kx^{k1})^{1} \mod p\]
I want to show:
\[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k1}(ypq)^i \equiv x^k+kypqx^{k1}\]
the congruence is mod n
 2 years ago
 2 years ago
I have the following information: \[n=p^2q\] \[k \ge 4\] \[0<v<n\] \[0 \le x < pq\] \[y=\lceil \frac{(vx^k) \mod n}{pq} \rceil \cdot (kx^{k1})^{1} \mod p\] I want to show: \[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k1}(ypq)^i \equiv x^k+kypqx^{k1}\] the congruence is mod n
 2 years ago
 2 years ago

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satellite73Best ResponseYou've already chosen the best response.0
i can't even read this what class?
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
i made a mistake \[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{ki}(ypq)^i \equiv x^k+kypqx^{k1}\] I'm trying to follow a proof but i don't know how they got from that one part to the other part
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
yeah well i cannot read what it says. good luck
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
http://www.cacr.math.uwaterloo.ca/hac/ its in chapter 11 on page 473 at the bottom
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
i wonder if james or zarkon could do it
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.0
ask me next semester when I've taken cryptography, and I might be able to help you, but right now, I haven't got a clue.
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
only the first two values of i will matter (i=0,1) for i>1 you have a \((pq)^2\) part which is \(p^2qq=nq\) which is zero nod n
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
i don't see this (pq)^2 part
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
george what kind of math have you had?
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
\[{k\choose i}x^{k1}(ypq)^i\] for \(i\ge2\) \[{k\choose i}x^{k1}(ypq)^i={k\choose i}x^{k1}(y^i)(pq)^{i2}p^2qq\] \[=\left({k\choose i}x^{k1}(y^i)(pq)^{i2}q\right)\times n\]
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
you are so smart to notice the first two values will only matter since n mod n is like totally 0 thanks zarkon
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.0
I've only had a year and a half of college level math so far, so that means, calc 13, lin. algebra, abstract algebra, and analysis
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
is there any number theory in abstract algebra i can't remember
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.0
not very much. I'm taking intro to number theory, and cryptography next semester.
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
number theory is so cool and interesting to me although my skills suck right now
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.0
It certainly sounds fun. I'm definitely enjoying my abstract algebra class right now. We had the barest hints of some number theory in discrete math so I'm not completely helpless.
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
i like these math puzzles
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
differential equations is not as fun to me but i do like the remedial kind lol
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
zarkon do you think there is hope for my brain?
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.0
From my experience, I don't like differential equations very much. Granted, I've never had a full course in it, but it just isn't my thing.
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
i feel like i'm trapped inside with an apes' brain
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
thanks i take that as a compliment
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
If you want a fun class...Take a course in measure theoretic probability theory.
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
he says that because he is a stat nerd
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.0
I don't think my school has that class...
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
or a class in stochastic processes
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
sometimes it will fall under the title of applied probability
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
i think they might have that
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
i always had a 10 foot pole when it came to statistics i only had to put it down when the course in stat was required
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.0
I'm personally more of an algebra person. Stats was interesting at first, but then it got boring.
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
There are some cool things though in stat i do admit
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
There is plenty of really nice mathematics in statistics
 2 years ago

KingGeorgeBest ResponseYou've already chosen the best response.0
It was the same with calculus for me. Interesting at first, and then it just stopped interesting me.
 2 years ago

ZarkonBest ResponseYou've already chosen the best response.2
A lot of multivariate calculus and matrix theory
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
zarkon can i ask another question
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
this is my last problem with this proof...
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
omg never i got it lol
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
i was typing it all out then i realized oh yeah lol
 2 years ago

myininayaBest ResponseYou've already chosen the best response.0
ok i feel good about this proof thanks for all your help
 2 years ago
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